A Course in Computational Algebraic Number Theory

This book, written by one of the leading authorities in the field describes 148 algorithms that are fundamental for number-theoretic computations including computations related to algebraic number theory, elliptic curves, primality testing, and factoring. A complete theoretical introduction is given for each subject, reducing prerequisites to a minimum. The detailed description of each algorithm allows immediate computer implementation ; numerous further hints for implementation are also provided.
Many of the algorithms have never been published or appear here for the first time in book form. The first seven chapters lead the reader to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, and for elliptic curve computations. The last three chapters give a survey of factoring and primality testing methods, including a detailed description of the number-field sieve algorithm.
The book ends with a description of available computer packages and some useful tables. It contains a large number of exercises.